In general, magnetic resonance imaging (MRI) examinations are based on the interactions among a primary magnetic field, a radiofrequency (RF) magnetic field, and time varying magnetic gradient fields with gyromagnetic material having nuclear spins within a subject of interest, such as a patient. Certain gyromagnetic materials, such as hydrogen nuclei in water molecules, have characteristic behaviors in response to external magnetic fields. The precession of spins of these nuclei can be influenced by manipulation of the fields to produce RF signals that can be detected, processed, and used to reconstruct a useful image.
In MRI, the signals that are detected are used to fill k-space, which is in a general sense related to an MR image by a Fourier transform. Generally, k-space contains encoded data and when transformed into the image space, is complex—it includes both magnitude and phase. Each of the magnitude and the phase can be reconstructed to produce respective images.
Unfortunately, the signals collected during MRI sequences will almost certainly include noise and certain distortions (e.g., due to fluctuations in magnetic field or movement), which if left uncorrected can reduce image quality. Various techniques have been developed to enhance image quality by increasing the signal-to-noise ratio (SNR) of the acquired data while reducing image distortions. However, such techniques may be inadequate or are subject to further improvement.